John, even though Wiki cites a Harvard publication, you'll notice that what it says squares with what I wrote. The estimates are based on inferences from surnames rather than on direct evidence:

"The ancestry of the 3,929,326 million population in 1790 has been estimated by various sources by sampling last names in the 1790 census and assigning them a country of origin. According to the Harvard Encyclopedia of American Ethnic Groups (Thernstrom, S 1980, 'Irish,' p. 528), there were 400,000 Americans of Irish birth or ancestry in 1790; half of these were descended from Ulster, and half were descended from the other provinces of Ireland."

And how culturally significant is "Irish ancestry" - much less Scotch-Irish - when all there is to go on is a surname? If one parent is Irish and another English, Scottish, or Welsh, which category fits?

Wiki's source is dated 1980. I read about the sampling bias in the late '90s. Wish I could remember where. (Some big red book with lots of demographic articles. Maybe it'll come to me.)